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What does decidability mean?

Looking for the meaning or definition of the word decidability? Here's what it means.

Noun
  1. (logic) the state or condition of being decidable.
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Performance evaluation was done with decidability, EER, DET curve shown better performance than other methods.
Both the decidability results and undecidablity results extend in various ways to Boolean algebras in extensions of first-order logic.
Decidability results: testing unboundedness of FIFO queues, temporal logic.
Moreover, these decidability results can be used to perform an under-approximation analysis to effectively detect bad behaviors of the analyzed programs.
We investigate decidability problems and prove that some properties that are undecidable for general context-free languages become decidable for XML-languages.
An ambitious goal would be to establish the decidability of first order theory in virtually free groups.

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